Relations between the former US vice-presidential candidate Sarah Palin and Levi Johnston, the teenager who almost became her son-in-law, have deteriorated to the point that a court battle is now inevitable, he has told the Guardian.

The dispute is over Tripp, his infant son by Palin's eldest daughter, Bristol: he claims Palin is preventing him from seeing the child.

"I'm up to the point where I can't see my kid again. I'm done. I'm sure we'll end up in court. We're definitely going to court," Johnston, 19, said in an interview in Anchorage, Alaska's largest city.

Johnston was propelled to national and international media attention last September when it was revealed he had made Bristol, who was then 17 and still at school, pregnant.

The disclosure was made just days after Palin was chosen as John McCain's Republican vice-presidential running mate in the presidential election.

Tripp was born on 27 December, but the couple broke up less than three months later. Since then, Johnston and the Palin family have been locked in an increasingly acrimonious debate about access.

Johnston said there had been times when he had been allowed to see Tripp about once a week, but there had also been periods when he had had virtually no access. He said: "They started letting me see him and everything was fine. But everything got bad again. So I said screw them."

Johnston said his relationship with the Palin family was entering another bad phase where his calls were not being returned, even though he said he was now paying child support.

He has not seen Tripp for several weeks, and he blamed Sarah Palin personally for that: "Bristol listens to her mom. Sarah says something, Bristol is going to follow."

An ugly court dispute is unlikely to be an attractive proposition for Palin, either as Bristol's mother or as a politician with a book launch pending and a possible run at the presidency in 2012. A large part of Palin's political appeal rests on her reputation for being a homely "hockey mum" that could be tarnished by a public custody fight.

Johnston said he recognised that taking the legal road would be hard. "It's going to be a tough battle. Basically, it's down to who has the better lawyer. I can just imagine all the cameras that are going to be there – it's going to be crazy," he said.

Palin has responded to Johnston's recent criticisms by using the American media to accuse him of peddling flat-out lies and exaggerations, adding it was unfortunate that he chose to exploit his former relationship with Bristol than care for the wellbeing of their child.

Sarah Palin's lawyer, Thomas Van Flein, said: "Other than noting that Tripp's father is always welcome to visit his son, we are unable to respond to these allegations as it is inappropriate to discuss child custody matters publicly."

Johnston admitted to the Guardian that comments he made to Vanity Fair and other outlets calling Palin a distant mother and a political hypocrite were partly made in retaliation. "If they had let me see my kid, I wouldn't have done any of that."

Asked whether he worried that his outspoken remarks about Tripp's grandmother might be harmful to the child, he replied: "I don't know. I hope not, but what else are you going to do?"

Rex Butler, a lawyer who is acting as Johnston's media agent, said his client had given statements that were not flattering to Sarah Palin "but he's never been malicious. Of course, the Palins and Palin supporters would like to discredit him."

Palin's memoir, Going Rogue, will be published on 17 November and is already in the bestseller lists. It has earned her at least $1.5m (£910,000) in advances.